Interesting Pattern - 43 - Square of three digit number with zero as the middle digit

I am sure this is something which most of you are aware but it is worth a re-cap given the simplicity

Square of numbers with Zero as the middle digit

Start with 100's

1.) 104 * 104 = 10816

How do we arrive at this without going through usual multiplication steps

1*1 = 1, 4* (1+1) = 08, 4*4 = 16

Append them together and you get  10816

Alternate way to get the answer (have explained why this is required for few other scenarios in 5 and 6)

1
  08
      16
--------
10816

2.) 107 * 107 = 11449

1*1 = 1, 7 * (1+1) = 14, 7*7 = 49

3.) 204 * 204

2*2 = 4, 4 *(2+2) = 16, 4*4 = 16

Answer = 41616

4.) 209 * 209

2*2 =4, 9*(2+2) = 36, 9 * 9 = 81

Answer - 43681

It becomes a bit tricky when the middle value exceeds 2 digits like in the examples below. But all that's required is to shift that by one place and add instead of concatenation

5) 906 * 906

9*9 = 81, 6*(9+9) = 108, 6*6 = 36

81
  108
        36
--------
820836

6) 809* 809

8*8 = 64, 9*(8+8) = 144, 9*9 = 81

64
  144
        81
---------
654481


Anyway, some patterns are meant to be broken somewhere but its all fun as far as Maths is concerned and especially Numbers :)

Interesting Multiplication pattern ----> 42

Check these out...

23 * 103 = 2369 ----> 23 * 3 = 69 (obvious since we have multiplied 23 with (100 + 3)

Now reverse of 2369 is 9632 ----> 96/3 =32

34 * 102 = 3468 ----> 34 * 2 = 68 (again expected)

Now reverse of 3468 is 8643 ----> 86/2 = 43!

How many such patterns you can find? And any reason for some of the numbers showing this pattern?